Editing Mathematical morphology (section)

{{Short description|Theory and technique for handling geometrical structures}}
{{More footnotes needed
|date=June 2024}}
[[File:DilationErosion.png|thumb|right|A shape (in blue) and its morphological dilation (in green) and erosion (in yellow) by a diamond-shaped structuring element.]]
'''Mathematical morphology''' ('''MM''') is a theory and technique for the analysis and processing of [[Geometry|geometrical]] structures, based on [[set theory]], [[lattice theory]], [[topology]], and [[random function]]s. MM is most commonly applied to [[digital image]]s, but it can be employed as well on [[Graph (discrete mathematics)|graphs]], [[polygon mesh|surface meshes]], [[Solid geometry|solids]], and many other spatial structures.

[[Topology|Topological]] and [[Geometry|geometrical]] [[continuum (theory)|continuous]]-space concepts such as size, [[shape]], [[convex set|convexity]], [[Connectedness|connectivity]], and [[geodesic distance]], were introduced by MM on both continuous and [[discrete space]]s. MM is also the foundation of morphological [[image processing]], which consists of a set of operators that transform images according to the above characterizations.

The basic morphological operators are [[Erosion (morphology)|erosion]], [[Dilation (morphology)|dilation]], [[Opening (morphology)|opening]] and [[Closing (morphology)|closing]].

MM was originally developed for [[binary image]]s, and was later extended to [[grayscale]] [[Function (mathematics)|functions]] and images. The subsequent generalization to [[complete lattice]]s is widely accepted today as MM's theoretical foundation.